#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Periodic_3_triangulation_traits_3.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Periodic_3_triangulation_traits_3<K>          PK;
typedef CGAL::Periodic_3_Delaunay_triangulation_3<PK>       P3DT3;

typedef PK::Point_3        Point;
typedef PK::Triangle_3     Triangle;

typedef P3DT3::Periodic_triangle           Periodic_triangle;
typedef P3DT3::Periodic_triangle_iterator  Periodic_triangle_iterator;
typedef P3DT3::Iterator_type               Iterator_type;

int main() {
  P3DT3 T;

  T.insert(Point(0,0,0));
  T.insert(Point(0,0,0.5));
  T.insert(Point(0,0.5,0.5));
  T.insert(Point(0.5,0,0.5));

  Periodic_triangle pt;
  Triangle t_bd;

  // Extracting the triangles that have a non-empty intersection with
  // the original domain of the 1-sheeted covering space
  for (Periodic_triangle_iterator ptit = T.periodic_triangles_begin(P3DT3::UNIQUE_COVER_DOMAIN);
       ptit != T.periodic_triangles_end(P3DT3::UNIQUE_COVER_DOMAIN); ++ptit) {
    pt = *ptit;
    if (! (pt[0].second.is_null() && pt[1].second.is_null() && pt[2].second.is_null()) ) {
      // Convert the current Periodic_triangle to a Triangle if it is
      // not strictly contained inside the original domain.
      // Note that this requires EXACT constructions to be exact!
      t_bd = T.construct_triangle(pt);
    }
  }
}